{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" Tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau c\u1ea1nh-g\u00f3c-c\u1ea1nh c\u1ee7a hai tam gi\u00e1c l\u00e0: ","select":[" A. N\u1ebfu hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. "," B. N\u1ebfu hai c\u1ea1nh v\u00e0 m\u1ed9t g\u00f3c c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng hai c\u1ea1nh v\u00e0 m\u1ed9t g\u00f3c c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. "," C. N\u1ebfu hai c\u1ea1nh v\u00e0 g\u00f3c k\u1ec1 c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng hai c\u1ea1nh v\u00e0 g\u00f3c k\u1ec1 c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. ","D. N\u1ebfu hai g\u00f3c v\u00e0 c\u1ea1nh xen gi\u1eefa c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng hai g\u00f3c v\u00e0 c\u1ea1nh xen gi\u1eefa c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. "],"explain":" Tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau c\u1ea1nh-g\u00f3c-c\u1ea1nh c\u1ee7a hai tam gi\u00e1c l\u00e0: <br\/> N\u1ebfu hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. <br\/><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span>","column":1}]}],"id_ques":1611},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Hai tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau l\u00e0 hai tam gi\u00e1c vu\u00f4ng c\u00f3: ","select":[" A. G\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng g\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n c\u1ee7a tam gi\u00e1c vu\u00f4ng kia. "," B. Hai g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng kia. "," C. Hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia. ","D. M\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng kia. "],"explain":" <span class='basic_left'> Hai tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau l\u00e0 hai tam gi\u00e1c vu\u00f4ng c\u00f3: <br\/> Hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia. <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> <\/span>","column":1}]}],"id_ques":1612},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["45"],["45"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> V\u1ebd tam gi\u00e1c $ABC$ bi\u1ebft $\\widehat{A} = 90^{o} $, $AB = AC = 4cm.$ <br\/> Sau \u0111\u00f3 \u0111o c\u00e1c g\u00f3c $B$ v\u00e0 $C$. <br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $\\widehat{B} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} \\\\ \\widehat{C} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ <\/span>","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-01.png' \/><\/center> <span class='basic_left'> - V\u1ebd g\u00f3c $\\widehat{xAy} = 90^{o} $ <br\/> - Tr\u00ean tia Ax v\u1ebd \u0111o\u1ea1n th\u1eb3ng $AB = 4cm$ <br\/> - Tr\u00ean tia Ay v\u1ebd \u0111o\u1ea1n th\u1eb3ng $AC = 4cm$ <br\/> - V\u1ebd \u0111o\u1ea1n th\u1eb3ng BC. <br\/> D\u00f9ng th\u01b0\u1edbc \u0111o g\u00f3c ta \u0111o \u0111\u01b0\u1ee3c $\\widehat{B} = \\widehat{C} = 45^{o} $ <\/span> "}]}],"id_ques":1613},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"N\u00eau th\u00eam m\u1ed9t \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $\\triangle ABC = \\triangle ADC $ theo tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh-g\u00f3c-c\u1ea1nh. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-03.png' \/><\/center> ","select":[" A. $BC = DC $ "," B. $\\widehat{ABC} = \\widehat{ADC} $"," C. $\\widehat{BAC} = \\widehat{DAC} $ ","D. $\\widehat{BCA} = \\widehat{DCA} $ "],"explain":" <span class='basic_left'> Tr\u00ean h\u00ecnh v\u1ebd ta c\u00f3: <br\/> + $AB = AD$ <br\/> + C\u1ea1nh AC chung <br\/> \u0110\u1ec3 $\\triangle ABC = \\triangle ADC$ (c . g . c) th\u00ec ta c\u1ea7n th\u00eam \u0111i\u1ec1u ki\u1ec7n $\\widehat{BAC} = \\widehat{DAC} $ (g\u00f3c xen gi\u1eefa) <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":1614},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"N\u00eau th\u00eam m\u1ed9t \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $\\triangle CAB = \\triangle DBA $ theo tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh-g\u00f3c-c\u1ea1nh. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-04.png' \/><\/center> ","select":[" A. $BC = AD $ "," B. $\\widehat{ACB} = \\widehat{BDA} $"," C. $AB = AC $ ","D. $AC = BD $ "],"explain":" Th\u00eam $AC = BD $ th\u00ec $\\triangle CAB = \\triangle DBA $ (c.g.c) <br\/><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span>","column":2}]}],"id_ques":1615},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho h\u00ecnh v\u1ebd, <br\/> C\u00f3 c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau l\u00e0: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-06A.png' \/> <img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-06B.png' \/><\/center> ","select":[" A. $\\triangle{ABC} = \\triangle{KDE} $ "," B. $\\triangle{ABC} = \\triangle{NMP} $"," C. $\\triangle{KDE} = \\triangle{NMP} $","D. $\\triangle{ABC} = \\triangle{KDE} = \\triangle{NMP} $ "],"explain":" <span class='basic_left'> Ta t\u00ednh \u0111\u01b0\u1ee3c $\\widehat{D} = 180^{o} - 80^{o} - 40^{o} = 60^{o}$ <br\/> $\\triangle ABC = \\triangle KDE $ c\u00f3: <br\/> + $AB = KD$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{B} = \\widehat{D} (=60^{o}) $ <br\/> + $BC = DE$ (gi\u1ea3 thi\u1ebft) <br\/> Do \u0111\u00f3 $\\triangle ABC = \\triangle KDE $ (c.g.c) <br\/> C\u00e2u B. $\\triangle ABC $ kh\u00f4ng b\u1eb1ng $\\triangle NMP $ v\u00ec \u0111\u1ec1 b\u00e0i kh\u00f4ng cho $BC = MP$ <br\/> C\u00e2u C. $\\triangle KDE $ kh\u00f4ng b\u1eb1ng $\\triangle NMP $ v\u00ec \u0111\u1ec1 b\u00e0i kh\u00f4ng cho $DE = MP$ <br\/><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span> <\/span>","column":2}]}],"id_ques":1616},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho \u0111o\u1ea1n th\u1eb3ng $AB$, \u0111i\u1ec3m M n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a AB. <br\/> So s\u00e1nh \u0111\u1ed9 d\u00e0i c\u00e1c \u0111o\u1ea1n th\u1eb3ng $MA$ v\u00e0 $MB$ ","select":[" $MA < MB$ "," $MA = MB$ "," $MA > MB$ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-07.png' \/><\/center> <span class='basic_left'> Do $MH$ l\u00e0 trung tr\u1ef1c c\u1ee7a AB (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{MHA} = \\widehat{MHB} = 90^{o} $ v\u00e0 $AH=HB$ <br\/> X\u00e9t $\\triangle MAH $ v\u00e0 $\\triangle MHB $ c\u00f3: <br\/> + $MH$ c\u1ea1nh chung <br\/> + $\\widehat{MHA} = \\widehat{MHB} = 90^{o} $ (\u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> + $HA = HB$ (ch\u1ee9ng minh tr\u00ean) <br\/> Do \u0111\u00f3 $\\triangle MHA = \\triangle MHB $ (c.g.c) <br\/> Suy ra $MA = MB$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <\/span> ","column":3}]}],"id_ques":1617},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-13.png' \/><\/center> <br\/> Cho tam gi\u00e1c $GIK$, v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng d \u0111i qua G v\u00e0 song song v\u1edbi $IK$. Tr\u00ean d l\u1ea5y \u0111i\u1ec3m H sao cho $GH = IK$ (H v\u00e0 I n\u1eb1m tr\u00ean hai n\u1eeda m\u1eb7t ph\u1eb3ng \u0111\u1ed1i nhau c\u00f3 b\u1edd ch\u1ee9a c\u1ea1nh GK). Khi \u0111\u00f3 \u0111\u00e1p \u00e1n n\u00e0o sau \u0111\u00e2y sai: <\/span> ","select":[" A. $\\triangle GIK > \\triangle KHG $ "," B. $GI = KH $"," C. $GI \/\/ KH $","D. $ \\widehat{GIK} = \\widehat{KHG} $ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-13.png' \/><\/center> <span class='basic_left'> \u0110\u00e1p \u00e1n A Sai. V\u00ec ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c ngay $\\triangle GIK = \\triangle KHG $. <br\/> Do 2 tam gi\u00e1c n\u00e0y c\u00f3 chung 1 c\u1ea1nh GK, g\u00f3c $\\widehat{IKG}$ = $\\widehat{HGK}$ do GH\/\/IK v\u00e0 C\u1ea1nh GH=IK - tr\u01b0\u1eddng h\u1ee3p C\u1ea1nh, G\u00f3c, C\u1ea1nh<br\/> Do \u0111\u00f3 \u0111\u00e1p \u00e1n D c\u0169ng l\u00e0 \u0111\u00fang (2 c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng c\u1ee7a 2 tam gi\u00e1c b\u1eb1ng nhau) <br\/> Ta c\u0169ng th\u1ea5y \u0111\u01b0\u1ee3c: $\\triangle GIK = \\triangle KHG $ <br\/> $\\Rightarrow GI=KH$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n B l\u00e0 \u0111\u00fang<\/b> <br\/> $\\Rightarrow \\widehat{IGK}=\\widehat{HKG}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> M\u00e0 $\\widehat{IGK}$ v\u00e0 $\\widehat{HKG}$ \u1edf v\u1ecb tr\u00ed so le trong v\u1edbi nhau <br\/> Do \u0111\u00f3: $GI \/\/KH$ $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C l\u00e0 \u0111\u00fang <\/b> <\/span> ","column":2}]}],"id_ques":1618},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd, bi\u1ebft $AB = AD, AC$ l\u00e0 c\u1ea1nh chung. <br\/> Ta c\u00f3 $\\triangle BAC = \\triangle DAC (c.g.c) $ khi: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-14.png' \/><\/center> <\/span> ","select":[" A. $\\widehat{BCA} = \\widehat{DCA} $ "," B. $\\widehat{BAC} = \\widehat{DAC} $"," C. $\\widehat{ABC} = \\widehat{ADC} $","D. $\\widehat{BAC} = \\widehat{ADC} $ "],"explain":"<span class='basic_left'> Tam gi\u00e1c $ABC$ v\u00e0 tam gi\u00e1c $ADC$ c\u00f3:<br\/> + $AB = AD$ (gi\u1ea3 thi\u1ebft), + $AC$ c\u1ea1nh chung<br\/> L\u1ea1i c\u00f3 $\\widehat{BAC}$ v\u00e0 $\\widehat{DAC}$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 g\u00f3c xen gi\u1eefa c\u1ee7a c\u00e1c c\u1eb7p c\u1ea1nh $AB$ v\u00e0 $AC, AD$ v\u00e0 $AC$. <br\/> Do \u0111\u00f3 \u0111\u1ec3 $\\Delta ABC=\\Delta ADC$ theo tr\u01b0\u1eddng h\u1ee3p c-g-c ta c\u1ea7n th\u00eam \u0111i\u1ec1u ki\u1ec7n: $\\widehat{BAC} = \\widehat{DAC} $ <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span> <\/span>","column":2}]}],"id_ques":1619},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho g\u00f3c nh\u1ecdn $xOy$. Tr\u00ean $Ox$ l\u1ea5y hai \u0111i\u1ec3m $A, C$, tr\u00ean $Oy$ l\u1ea5y hai \u0111i\u1ec3m $B, D$ sao cho $OA = OB, OC = OD$ ($A$ n\u1eb1m gi\u1eefa $O$ v\u00e0 $C, B$ n\u1eb1m gi\u1eefa $O$ v\u00e0 $D$). <br\/> So s\u00e1nh hai g\u00f3c $\\widehat{CAD} $ v\u00e0 $\\widehat{CBD} $ <\/span>","select":[" $\\widehat{CAD} < \\widehat{CBD} $ "," $\\widehat{CAD} = \\widehat{CBD} $ "," $\\widehat{CAD} > \\widehat{CBD} $ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-23.png' \/><\/center> <span class='basic_left'> X\u00e9t tam gi\u00e1c $\\triangle OAD $ v\u00e0 $\\triangle OBC $ c\u00f3: <br\/> + $OA = OB$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{O}$ chung <br\/> + $OD = OC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\triangle OAD = \\triangle OBC $ (c.g.c) <br\/> $\\Rightarrow \\widehat{OAD} = \\widehat{OBC} $ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> M\u00e0 $\\widehat{OBC} + \\widehat{CBD} = 180^{o}, \\widehat{OAD} + \\widehat{DAC} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> Suy ra $\\widehat{CAD} = \\widehat{CBD}$ <\/span> ","column":3}]}],"id_ques":1620},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$. Tr\u00ean n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd $BC$ c\u00f3 ch\u1ee9a \u0111i\u1ec3m A v\u1ebd tia $Bx$ vu\u00f4ng g\u00f3c v\u1edbi $BC$, tr\u00ean tia $Bx$ l\u1ea5y \u0111i\u1ec3m D sao cho $BD = BC$. Tr\u00ean n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd $AB$ c\u00f3 ch\u1ee9a \u0111i\u1ec3m C v\u1ebd tia $By$ vu\u00f4ng g\u00f3c v\u1edbi $AB$, tr\u00ean $By$ l\u1ea5y \u0111i\u1ec3m $E$ sao cho $BE = BA$. So s\u00e1nh $AD$ v\u00e0 $CE$. <\/span>","select":[" $AD < CE$ "," $AD = CE$"," $AD > CE$ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-28.png' \/><\/center> <span class='basic_left'> Ta c\u00f3: $\\widehat{B_{1}} + \\widehat{B_{2}} = 90^{o}$ v\u00e0 $\\widehat{B_{2}} + \\widehat{B_{3}} = 90^{o} $ <br\/> Suy ra $\\widehat{B_{1}} = \\widehat{B_{3}}$ <br\/> X\u00e9t $\\triangle ABD $ v\u00e0 $\\triangle EBC $ c\u00f3: <br\/>+ $ BD = BC$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{B_{1}} = \\widehat{B_{2}}$ (ch\u1ee9ng minh tr\u00ean) <br\/> + $BE = BA$ (gi\u1ea3 thi\u1ebft) <br\/> Do \u0111\u00f3 $\\triangle ABD = \\triangle EBC $ (c.g.c) <br\/> Suy ra $AD = CE$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <\/span> ","column":3}]}],"id_ques":1621},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"<span class='basic_left'> Qua trung \u0111i\u1ec3m M c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng d vu\u00f4ng g\u00f3c v\u1edbi $AB$. Tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng d l\u1ea5y hai \u0111i\u1ec3m H v\u00e0 K sao cho M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $HK$. <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh $AB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{HAK} $. <\/span> ","temp":"sequence","correct":[[[1],[3],[4],[2],[5]]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-50.png","left":["X\u00e9t $\\triangle AMH $ v\u00e0 $\\triangle AMK $ c\u00f3:","Do \u0111\u00f3 $\\triangle AMH = \\triangle AMK $ (hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng nhau)","Suy ra $\\widehat{MAH} = \\widehat{MAK} $ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) ","$\\widehat{AMH} = \\widehat{AMK} = 90^{o} $, c\u1ea1nh AM chung, MH = MK (gi\u1ea3 thi\u1ebft) ","V\u1eady AB l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{HAK} $ "],"top":55,"explain":"<span class='basic_left'>X\u00e9t $\\triangle AMH $ v\u00e0 $\\triangle AMK $ c\u00f3: <br\/>+ c\u1ea1nh AM chung <br\/> + $\\widehat{AMH} = \\widehat{AMK} = 90^{o} $ <br\/> + $MH = MK$ (gi\u1ea3 thi\u1ebft) <br\/> Do \u0111\u00f3 $\\triangle AMH = \\triangle AMK $ (hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng nhau) <br\/> Suy ra $\\widehat{MAH} = \\widehat{MAK} $ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> V\u1eady $AB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{HAK} $ <\/span> "}]}],"id_ques":1622},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ c\u00f3 $\\widehat{A} = 90^{o} $, tia ph\u00e2n gi\u00e1c $BD$ c\u1ee7a g\u00f3c $B (D \\in AC)$. Tr\u00ean c\u1ea1nh $BC$ l\u1ea5y \u0111i\u1ec3m E sao cho $BE = BA$. So s\u00e1nh \u0111\u1ed9 d\u00e0i hai \u0111o\u1ea1n th\u1eb3ng $AD$ v\u00e0 $DE$. <\/span>","select":[" $AD < DE$ "," $AD = DE$"," $AD > DE$ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-31.png' \/><\/center> <span class='basic_left'> Ta c\u00f3 BD l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c B n\u00ean: $\\widehat{B_{1}} = \\widehat{B_{2}} $ <br\/> X\u00e9t $\\triangle ABD $ v\u00e0 $\\triangle EBD $ c\u00f3: <br\/> + $BA = BE$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{B_{1}} = \\widehat{B_{2}}$ (gi\u1ea3 thi\u1ebft) <br\/> + c\u1ea1nh $BD$ chung <br\/> Do \u0111\u00f3 $\\triangle ABD = \\triangle EBD $ (c.g.c) <br\/> Suy ra $AD = DE$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <\/span> ","column":3}]}],"id_ques":1623},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC, AM$ l\u00e0 trung tuy\u1ebfn, tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $MA$ l\u1ea5y $A'$ sao cho $MA' = MA.$ <br\/> Khi \u0111\u00f3: $\\triangle ACA' = \\triangle A'BA $ <\/span>","select":[" \u0110\u00fang "," Sai"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-35.png' \/><\/center><span class='basic_left'> X\u00e9t $\\triangle MAB $ v\u00e0 $\\triangle MA'C $ c\u00f3: <br\/> + $MB = MC$ <br\/> + $\\widehat{M_{1}} = \\widehat{M_{2}} $ (\u0111\u1ed1i \u0111\u1ec9nh) <br\/> + $MA = MA'$ (gi\u1ea3 thi\u1ebft) <br\/> Do \u0111\u00f3 $\\triangle MAB = \\triangle MA'C $ (c.g.c) <br\/> $\\Rightarrow AB = A'C $ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u00f3 $AC = BA'.$ <br\/> X\u00e9t tam gi\u00e1c $ACA'$ v\u00e0 $A'BA$ c\u00f3: <br\/> + $AC = BA'$ <br\/> + $ A'C = AB$<br\/> + $AA'$ chung <br\/> V\u1eady $\\triangle ACA' = \\triangle A'BA $ (c.c.c) <\/span>","column":2}]}],"id_ques":1624},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-40.png' \/><\/center><br\/> Cho h\u00ecnh v\u1ebd bi\u1ebft $AB = AE, AD = AC, DE = 4cm.$ <br\/> \u0110\u1ed9 d\u00e0i c\u1ea1nh BC l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}(cm) $ ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-40.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle ABC $ v\u00e0 $\\triangle AED $ c\u00f3: <br\/> + $AB = AE$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{A} $ chung <br\/> + $AD = AC$ (gi\u1ea3 thi\u1ebft) <br\/> Do \u0111\u00f3 $\\triangle ABC = \\triangle AED $ (c.g.c) <br\/> $\\Rightarrow $ $ED = BC$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> M\u00e0 $ED = 4$(cm) (gi\u1ea3 thi\u1ebft) $\\Rightarrow $ $BC = 4$ (cm) <br\/> V\u1eady $BC = 4$ cm "}]}],"id_ques":1625},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> \u0110i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng (...) trong ph\u00e1t bi\u1ec3u sau \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang: <br\/> N\u1ebfu $\\triangle RSQ $ v\u00e0 $\\triangle DFE $ c\u00f3: <br\/> $\\widehat{R} = \\widehat{D} = 90^{o} $, $RS = DE, QR = FD$ th\u00ec ... <\/span> ","select":[" A. $\\triangle QRS = \\triangle FED $ "," B. $\\triangle QRS = \\triangle DEF $ "," C. $\\triangle RSQ = \\triangle DEF $ ","D. $\\triangle RSQ = \\triangle DFE $ "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-43.png' \/><\/center> <span class='basic_left'> N\u1ebfu $\\triangle RSQ $ v\u00e0 $\\triangle DFE $ c\u00f3: <br\/> + $RS = DE$ <br\/> + $\\widehat{R} = \\widehat{D} = 90^{o} $ <br\/> + $QR = FD$ <br\/> $\\Rightarrow \\triangle RSQ = \\triangle DEF $ (c.g.c) <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> <\/span>","column":2}]}],"id_ques":1626},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho $\\triangle SPQ $ v\u00e0 $\\triangle ACB $ c\u00f3 $PS = CA, PQ = CB$ <br\/> C\u1ea7n th\u00eam \u0111i\u1ec1u ki\u1ec7n g\u00ec \u0111\u1ec3 $\\triangle SPQ $ v\u00e0 $\\triangle ACB $ b\u1eb1ng nhau theo tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh-g\u00f3c-c\u1ea1nh? <\/span> ","select":[" A. $\\widehat{S} = \\widehat{A} $ "," B. $\\widehat{Q} = \\widehat{B} $ "," C. $\\widehat{Q} = \\widehat{C} $ ","D. $\\widehat{P} = \\widehat{C} $ "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-44.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle SPQ $ v\u00e0 $\\triangle ACB $ c\u00f3: <br\/> + $PS = CA$ <br\/>+ $\\widehat{P} = \\widehat{C} $ <br\/> + $ PQ = CB$ <br\/> $\\Rightarrow \\triangle SPQ = \\triangle ACB $ (c.g.c) <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span> <\/span>","column":2}]}],"id_ques":1627},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'> Cho $\\triangle BDC $ v\u00e0 $\\triangle KEF $ c\u00f3 $DB = EK$, $\\widehat{D} = \\widehat{K} $, $CD = KF$. <br\/> Ph\u00e1t bi\u1ec3u n\u00e0o trong c\u00e1c phi\u1ec3u sau l\u00e0 \u0111\u00fang? <\/span> ","select":[" A. $ \\triangle BDC = \\triangle EFK $ "," B. $ \\triangle BDC = \\triangle EKF $ "," C. $ \\triangle DBC = \\triangle EKF $ ","D. $ \\triangle BDC = \\triangle KEF $ "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-46.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle BDC $ v\u00e0 $\\triangle KEF $ c\u00f3: <br\/> + $DB = EK$ <br\/>+ $\\widehat{D} = \\widehat{K} $<br\/>+ $CD = KF$ <br\/> Do \u0111\u00f3 $ \\triangle BDC = \\triangle EKF $ (c.g.c) <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span> <\/span>","column":2}]}],"id_ques":1628},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'> Qua trung \u0111i\u1ec3m I c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$, k\u1ebb \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u1edbi $AB$, tr\u00ean \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c l\u1ea5y hai \u0111i\u1ec3m C v\u00e0 D. N\u1ed1i $CA, CB, DA, DB$. C\u00f3 m\u1ea5y c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau trong h\u00ecnh v\u1ebd? <\/span> ","select":[" A. 2 "," B. 3 "," C. 4 ","D. 5 "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-48.png' \/><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-49.png' \/><\/center> <span class='basic_left'> C\u00f3 ba c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau: <br\/> $\\triangle AIC = \\triangle BIC $ (c.g.c) v\u00ec c\u00f3: <br\/> + C\u1ea1nh $IC$ chung <br\/> $\\widehat {AIC} = \\widehat {BIC} = 90^o$ <br\/>+ $IA = IB$ (gi\u1ea3 thi\u1ebft) <br\/> Ta c\u00f3: $ \\triangle AID = \\triangle BID $ (c.g.c) v\u00ec c\u00f3: <br\/> + C\u1ea1nh $ID$ chung <br\/> + $\\widehat {AID} = \\widehat {BID} = 90^o$ <br\/> + $IA = IB$ (gi\u1ea3 thi\u1ebft) <br\/> Ta c\u00f3: $\\triangle ACD = \\triangle BCD $ (c.c.c) v\u00ec c\u00f3: <br\/> + $CA = CB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> + $DA = DB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> + C\u1ea1nh AB chung <br\/> V\u1eady c\u00f3 3 c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span> <\/span>","column":4}]}],"id_ques":1629},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'> Cho hai \u0111o\u1ea1n th\u1eb3ng BD v\u00e0 $CE$ vu\u00f4ng g\u00f3c v\u1edbi nhau t\u1ea1i A sao cho $AB = AE$, $AD = AC$, $AB < AC. $ Ph\u00e1t bi\u1ec3u n\u00e0o trong c\u00e1c ph\u00e1t bi\u1ec3u sau \u0111\u00e2y l\u00e0 sai? <\/span> ","select":[" A. $\\triangle AED = \\triangle ABC $ "," B. $BC = ED $ "," C. $EB = CD $ ","D. $EB \/\/ CD $ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai11/lv1/img\/H7B11-47.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle ABC$ v\u00e0 $\\triangle AED$ c\u00f3: <br\/> + $AB = AE$ <br\/> + $\\widehat {BAC} = \\widehat {EAD}$ <br\/>+ $ AC = AD$ <br\/> Suy ra $\\triangle ABC = \\triangle AED$ (c . g . c) <br\/> Suy ra: $BC = ED$ (c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> Tam gi\u00e1c $BAE$ c\u00f3: <br\/> + $AB = AE$<br\/> + $\\widehat {BAE} = 90^o$ <br\/> $\\Rightarrow$ $\\triangle ABE$ vu\u00f4ng c\u00e2n t\u1ea1i A <br\/> $\\Rightarrow$ $\\widehat {ABE} = \\widehat {AEB} = 45^o$ (1) <br\/> Tam gi\u00e1c $ACD$ c\u00f3: $AC = AD$, $\\widehat {CAD} = 90^o$ <br\/> $\\Rightarrow$ $\\triangle CAD$ vu\u00f4ng c\u00e2n t\u1ea1i A <br\/> $\\Rightarrow$ $\\widehat {ACD} = \\widehat {ADC} = 45^o$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $\\widehat {ABE} = \\widehat {ADC} = 45^o$ <br\/> M\u00e0 hai g\u00f3c n\u00e0y \u1edf v\u1ecb tr\u00ed so le n\u00ean $EB \/\/ CD$ <br\/> C\u00e2u sai l\u00e0 C. V\u00ec $\\triangle ABE $ kh\u00f4ng b\u1eb1ng $\\triangle ACD. $ ","column":2}]}],"id_ques":1630}],"lesson":{"save":0,"level":1}}